Block #615,494

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 7/4/2014, 1:46:20 AM · Difficulty 10.9404 · 6,194,043 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
c8e42b837dae1dbb2f0585d34907371901b968a6b936285a9a4e5fa51c06f87b

Height

#615,494

Difficulty

10.940449

Transactions

3

Size

659 B

Version

2

Bits

0af0c149

Nonce

35,584,846

Timestamp

7/4/2014, 1:46:20 AM

Confirmations

6,194,043

Merkle Root

c4a79b5ef799241e6f22285c54b6b1a3598f0e96c39b8c8c6e6d8a1e091f767c
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.246 × 10⁹⁴(95-digit number)
22465850878625922442…69396991803794881439
Discovered Prime Numbers
p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin − 1
2.246 × 10⁹⁴(95-digit number)
22465850878625922442…69396991803794881439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.493 × 10⁹⁴(95-digit number)
44931701757251844885…38793983607589762879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.986 × 10⁹⁴(95-digit number)
89863403514503689771…77587967215179525759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.797 × 10⁹⁵(96-digit number)
17972680702900737954…55175934430359051519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.594 × 10⁹⁵(96-digit number)
35945361405801475908…10351868860718103039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.189 × 10⁹⁵(96-digit number)
71890722811602951817…20703737721436206079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.437 × 10⁹⁶(97-digit number)
14378144562320590363…41407475442872412159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.875 × 10⁹⁶(97-digit number)
28756289124641180726…82814950885744824319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.751 × 10⁹⁶(97-digit number)
57512578249282361453…65629901771489648639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.150 × 10⁹⁷(98-digit number)
11502515649856472290…31259803542979297279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.300 × 10⁹⁷(98-digit number)
23005031299712944581…62519607085958594559
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,720,375 XPM·at block #6,809,536 · updates every 60s
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